1. Field of the Invention
The present invention relates to conversion of a color data value in a rectangular color coordinate system such as CIELab color coordinate system to a corresponding color data value in a cylindrical or polar coordinate system such as CIELCh coordinate system, and to in particular the use of one-dimensional look-up tables to facilitate the conversion.
2. Description of the Related Art
Recent efforts in implementation of color science into computer software have resulted in increasingly sophisticated and accurate applications, particularly at the consumer level. Correspondingly, end users of the software have increased expectations as to the accuracy and fidelity of color data reproduced thereby. For example, it is now commonplace for users to expect a color management system to accurately processes computerized color data such as color image data so as to maintain fidelity of the color data over a wide variety of viewing environments, and over a wide variety of output devices.
As a result of these increased expectations by users and the increased sophistication of applications, it is common for such applications to engage in significant manipulation of color data. One frequently encountered manipulation involves a transformation of color data from a rectangular coordinate system such as CIELab to cylindrical or polar coordinates such as CIELCh. For example, there are some manipulations such as gamut matching or mapping which is performed more easily and/or more accurately in cylindrical CIELCh coordinates, whereas there are other manipulations such as forward- and reverse-transforms based on device profiles that are better performed in rectangular coordinates such as CIELab.
Mathematically, the conversion of data values between CIELab and CIELCh coordinates involves the following equations (hereinafter, CIELab will be used as a representative example of rectangular coordinates and CIELCh will be used as a representative example of cylindrical or polar coordinates:                L=L        
                    L        =        L                                                            C        =                                            a              2                        +                          b              2                                                          (        1        )                                h        =                  arctan          ⁢                                          ⁢                      b            a                                              (        2        )            
These equations are computationally costly, particularly since the equations must be evaluated for each and every pixel in a color image. Other techniques have therefore been considered for evaluation of these equations in a less costly manner.
One such technique involves use of two-dimensional look-up tables, a first look-up table to evaluate the “C” value of equation (1) above, and a second look-up table to look up the “h” value in equation (2) above. Since each of these values depends on the “a” and “b” coordinates, a two-dimensional look-up table is required for each of equations (1) and (2).
This approach has significant disadvantages, particularly for look-up tables of reasonable size. For example, with a two-dimensional look-up table of 32×32 grid size, which requires 1,024 entries, an unacceptably large error value of nearly 10 degrees is obtained for the “h” value of equation (2). Although interpolation can help reduce this error, the error is still significant for table values of reasonable size, resulting in correspondingly significant color inaccuracies.